Gibaabaa means father's. It is not an object itself. Objects there are odasemaanza',
ojiimaan, etc.

In a statement:

Awenen gaa-mikawaad nizhooniyaaman? - Who found my money?

nizhooniyaman is obviative. A subject there - 'awenen' - 'who' is the third person
- he or she (check: who does it?; s/he does it), so nizhooniyaam
is an animate object, it's 'another he', so it must take an obviative suffix because of it.

Grammar note.

Body parts are dependent nouns in Ojibwe. They always stand in possessive form.
But despite kin terms some of body part terms are animate and some - inanimate nouns.